Figure REF  shows that the Doppler shift gradient smears the strong wavelength dependence of \(\dot{\tau }(r,\lambda )\) 
for the integrated extinction
and that the resulting absorption (bottom panel) has less structure.
However, in this example, there happens to be a clear downward slope in the extinction from 656.45 to 656.55 nm (\(\Delta v\approx 0\) –\(100~\mathrm {km}\,\mathrm {s^{-1}}\) ),
which exacerbates the asymmetry in the input line profileThis is partly due to a clear resonance near \(\lambda _{\mathrm {H}\,\alpha }+0.05\)  nm, present from large \(r\)  down to \(r\approx 4~R_{\mathrm {J}}\)  (\(T\approx 3000\) –4000 K). Comparing with [1]}, it likely comes from TiO or maybe VO..
The result is a crudely gaussian-looking blue wing but a linearly decreasing red wing. This leads to an apparent offset in the line peak but only by 25 \(\mathrm {km}\,\mathrm {s^{-1}}\) , much less than the line width.
